Timeline for On pairs of roots which are orthogonal but not strongly orthogonal

8 events

when toggle format	what		by	license	comment
Sep 12, 2016 at 8:40	vote	accept	Christoph Mark
Sep 10, 2016 at 17:33	comment	added	Christoph Mark		The question is indeed elementary, and I found a satisfactory answer on my own several hours later. You can delete the whole thing, if you want.
Sep 10, 2016 at 17:29	history	edited	Christoph Mark		edited tags
Sep 10, 2016 at 15:51	comment	added	Jim Humphreys		Probably this question is too elementary for this site (did you try stack exchange first?). In any case, it's useful to add a tag such as 'lie-algebras' so the question doesn't get overlooked. (Even though the question itself doesn't involve simple Lie algebras directly, that's where the root system ideas originated.)
Sep 10, 2016 at 15:20	comment	added	Victor Protsak		In type $C_n$, the roots are $2e_i$, $\pm e_i \pm e_j$ ($i<j$). Thus for $i \ne j$, $\alpha=e_i+e_j$ and $\beta=e_i-e_j$ are orthogonal, but not strongly orthogonal.
Sep 10, 2016 at 6:25	answer	added	Christoph Mark		timeline score: 1
Sep 9, 2016 at 17:36	comment	added	Christoph Mark		For my purposes it would be actually sufficient to replace the equality $(\alpha+\beta)^\vee=\alpha^\vee+\beta^\vee$ in Question 1 and Question 2 by the inequality $(\alpha+\beta)^\vee\leq\alpha^\vee+\beta^\vee$ where $\leq$ is the usual partial order on $\mathbb{Z}\Delta$ resp. $\mathbb{Z}\Delta^\vee$.
Sep 9, 2016 at 16:55	history	asked	Christoph Mark	CC BY-SA 3.0